Mathematical modeling of human cardiovascular and respiratory systems plays an important role in providing accurate diagnostic information about the cardiovascular-respiratory diseases. The mechanisms of the cardiovascular and respiratory systems are highly interconnected with each other. We study the control mechanism of the cardiovascular-respiratory system during the transition from awake state to stage 4 non-REM sleep state. A discrete-time cardiovascular-respiratory system model with transport delays is adopted. The system model is nonlinear and described by a set of higher order difference equations. We convert the system into a set of first-order difference equations and propose an iterative algorithm to find the optimal control inputs that drive the cardiovascular-respiratory system from awake state to sleep state. In each iteration, the system is linearized using the state and input sequences from the previous iteration. Simulations are conducted to demonstrate the effectiveness of the proposed method. The simulation results are validated using real data collected from a healthy subject.